Look at the installation manual that came with the solar panel. Note the maximum power voltage in volts and the maximum power current in amps. If the maximum voltage is between 16 and 19 volts, the panel is designed to charge a 12-volt battery. If the panel produces between 30 and 40 volts, it is designed for a 24-volt system. A photovoltaic system intended to power household appliances should be designed for 24 volts. Check that your solar panel is set up for 24 volts.
Place two 12-volt batteries and a 24-volt battery charge controller inside the house in a well-ventilated space. Measure the distance in feet from the solar panel to the batteries. tracing the line the connecting wires will follow. Multiply this distance by two.
Read the label on the back of the microwave. It will tell you how much power in watts the microwave uses. If other household appliances are to be operated at the same time, check the power of each appliance in turn and add up the total amount of power in watts that you will need to provide from the batteries.
Determine what size inverter you will need. The inverter will convert 12-volt DC electricity from the batteries to 110-volt AC electricity that will power the appliances. Inverters are rated according to the power in watts they provide. As an example, if the total power required by the appliances is 1,400 watts, then choose a 24-volt inverter rated for continuous operation at not less than 1,400 watts. Decide where you are going to install the inverter -- usually not too far from the appliances. Measure the distance in feet between the charge controller and the inverter. Multiply this distance by two and add this number of feet to the length of wire you calculated in step 2.
Buy the total length of copper cable you calculated. It is very important to buy the right thickness or gauge of copper cable. Check what the equipment supplier recommends and purchase this gauge of wire.
Connect the negative terminal of the first battery to the positive terminal of the second battery with the battery interconnect cable. If you have bought four 6-volt batteries, you must link them together in series using three interconnect cables.
Mount the charge controller on a wall close to the batteries. Cut the copper wire into two equal lengths. Connect the solar panel to the charge controller following the instructions in the controller manual. Connect the controller to the batteries. Switch on the charge controller and check that it is working correctly. The charge controller will show the voltage of the batteries.
Mount the inverter on a wall inside the house close to where you want to operate the microwave oven. Read the instruction manual that came with the inverter and connect the inverter to the terminals inside the charge controller that are marked "load." Switch on the inverter and check that it is working correctly.
Give the batteries a day to get charged when there is plenty of sunshine. Connect the household appliances one at at time to the inverter, starting with the appliance that takes the least amount of power. Small appliances should work fine. But appliances that take a lot of power, like a microwave oven, may not work for long before the battery voltage falls and the charge controller cuts off the power to the inverter.